On stabilizability and sampling for infinite dimensional systems

Some questions, either motivated by or related to time sampling, regarding the stabilizability of infinite-dimensional or distributed parameter systems are considered. In particular, these include the characteristics of those systems which are finite rank stabilizable, and the preservation of stabilizability under sampling. A pathological class of systems, which, when sampled, may be rendered unstabilizable by arbitrarily small perturbations in the sampling rate, is identified. The approach taken in establishing these results is based upon a spectral decomposition of the infinitesimal generator of the underlying open-loop semigroup. The results obtained apply to control systems with dynamics described by broad classes of partial and functional differential equations that arise frequently in applications.<
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